Spatiotemporal instabilities of counterpropagating beams in nematic liquid crystals

We investigate the behavior of counterpropagating self-trapped optical beam structures in nematic liquid crystals. We treat numerically a time-dependent model for the beam propagation and the director reorientation in a nematic liquid crystal, in (2 + 1) spatial dimensions. The formation of stable solitons in a narrow threshold region of control parameters is displayed. Spatiotemporal instabilities are observed as the input intensity, the propagation distance, and the birefringence are increased. Transverse displacement, filamentation, and dynamical instabilities of counterpropagating beams are demonstrated.